The 'Angels' singer's father Pete Conway told The Sun that Williams is overwhelmed by the news.
Conway commented: "He says he's been crying a lot because he's so pleased."
Meanwhile, Conway also revealed that the couple are considering calling the baby Pete, if it turns out to be a boy.
"Mark's expecting and Gary, so there will be three little Take That babies in one go. They might call it Pete," Conway added.
Following rumours that the unborn child is female, Williams yesterday wrote on his website that they are not yet aware of the baby's sex.
Watch the video for Robbie Williams classic 'Feel' below: